Finite Group Databasebeta

← C3×#25508 #10644115

Subgroups — C3×#25508 #10644115

Order 768.

1198 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#540C211yesmaximal, characteristic, complemented
2C2×C3×#469C211yesmaximal, characteristic, complemented
3C2×C3×#466C211yesmaximal, characteristic, complemented
4C3×#2624C211yesmaximal, characteristic, complemented
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2041C211yesmaximal, characteristic, complemented
7C3×#2025C211yesmaximal, characteristic, complemented
8C3×#2011C211yesmaximal, characteristic, complemented
9C3×#1895C211yesmaximal, characteristic, complemented
10C3×#1893C211yesmaximal, characteristic, complemented
11C3×#1879C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic, complemented
13C3×#1864C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic, complemented
15C3×#1729C211yesmaximal, characteristic, complemented
16#25508C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C23×C3×C8C2211yescharacteristic
21C3×#540—24no—
22C3×#540—24no—
23C2×C3×#127C2211yescharacteristic
24C2×C3×#125C2211yescharacteristic
25C2×C3×#123—21no—
26C2×C3×#123—21no—
27C2×C3×#121—21no—
28C2×C3×#121—21no—
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×C4×D4C2211yescharacteristic
34C2×C3×#117C2211yescharacteristic
35C3×#469—24no—
36C3×#466—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#106C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C3×#399—21no—
48C3×#397—21no—
49C3×#394—21no—
50C3×#394—21no—
51C3×#390C2211yescharacteristic
52C3×#390C2211yescharacteristic
53C3×#389C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#540C2×C311yescharacteristic, complemented
65C2×#469C2×C311yescharacteristic, complemented
66C2×#466C2×C311yescharacteristic, complemented
67#2624C2×C311yescharacteristic, complemented
68#2059C2×C311yescharacteristic, complemented
69#2041C2×C311yescharacteristic, complemented
70#2025C2×C311yescharacteristic, complemented
71#2011C2×C311yescharacteristic, complemented
72#1895C2×C311yescharacteristic, complemented
73#1893C2×C311yescharacteristic, complemented
74#1879C2×C311yescharacteristic, complemented
75#1879C2×C311yescharacteristic, complemented
76#1864C2×C311yescharacteristic, complemented
77#1862C2×C311yescharacteristic, complemented
78#1729C2×C311yescharacteristic, complemented
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4—21no—
84C22×C3×D4C2311yescharacteristic
85C22×C3×D4C2311yescharacteristic
86C22×C3×D4C2311yescharacteristic
87C23×C3×C4—21no—
88C23×C3×C4—21no—
89C23×C3×C4C2311yescharacteristic
90C2×C3×D8—22no—
91C2×C3×D8—22no—
92C2×C3×D8—22no—
93C2×C3×D8—22no—
94C2×C3×D8—41no—
95C2×C3×D8—41no—
96C2×C3×M16—22no—
97C2×C3×M16—22no—
98C2×C3×M16—41no—
99C22×C3×C8—22no—
100C22×C3×C8—22no—
101C22×C3×C8—41no—
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×#127—22no—
107C3×#127—22no—
108C3×#125—22no—
109C3×#125—22no—
110C3×#123—28no—
111C3×#123—28no—
112C3×#121—28no—
113C3×#121—28no—
114C3×#121—22no—
115C3×#121—22no—
116C3×#121—22no—
117C3×#121—22no—
118C3×#121D414yes—
119C3×#121D414yes—
120C3×C4×D4—22no—
121C3×C4×D4—22no—
122C3×C4×D4—22no—
123C3×C4×D4—22no—
124C3×#117—22no—
125C3×#117—22no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4D411yescharacteristic
131C2×C3×C4⋊C4D411yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4D411yescharacteristic
148C2×C3×C22⋊C4D411yescharacteristic
149C2×C3×C42C2311yescharacteristic
150C2×C3×C42C2311yescharacteristic
151C3×#107—22no—
152C3×#106—22no—
153C3×#102—22no—
154C3×#102—22no—
155C3×#102—22no—
156C3×#102—22no—
157C3×#102—22no—
158C3×#102—22no—
159C3×#102—41no—
160C3×#102—41no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C22×D8C22×C311yescharacteristic
165C22×D8C22×C311yescharacteristic
166C22×M16C22×C311yescharacteristic
167C23×C8C22×C311yescharacteristic
168#540—24no—
169#540—24no—
170C2×#127C22×C311yescharacteristic
171C2×#125C22×C311yescharacteristic
172C2×#123—21no—
173C2×#123—21no—
174C2×#121—21no—
175C2×#121—21no—
176C2×#121C22×C311yescharacteristic
177C2×#121C22×C311yescharacteristic
178C2×#121C22×C311yescharacteristic
179C2×C4×D4C22×C311yescharacteristic
180C2×C4×D4C22×C311yescharacteristic
181C2×#117C22×C311yescharacteristic
182#469—24no—
183#466—24no—
184C2×#107C22×C311yescharacteristic
185C2×#106C22×C311yescharacteristic
186C2×#102C22×C311yescharacteristic
187C2×#102C22×C311yescharacteristic
188C2×#102C22×C311yescharacteristic
189C2×#102C22×C311yescharacteristic
190C2×#102C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194#399—21no—
195#397—21no—
196#394—21no—
197#394—21no—
198#390C22×C311yescharacteristic
199#390C22×C311yescharacteristic
200#389C22×C311yescharacteristic
201#389C22×C311yescharacteristic
202#380C22×C311yescharacteristic
203#340C22×C311yescharacteristic
204#340C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#336C22×C311yescharacteristic
208#336C22×C311yescharacteristic
209#336C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C2×C3×D4—24no—
216C2×C3×D4—24no—
217C2×C3×D4—24no—
218C2×C3×D4—24no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—42no—
236C2×C3×D4—81no—
237C2×C3×D4—81no—
238C2×C3×D4—81no—
239C2×C3×D4—81no—
240C2×C3×D4—81no—
241C2×C3×D4—81no—
242C2×C3×D4—81no—
243C2×C3×D4—81no—
244C2×C3×D4—81no—
245C2×C3×D4—81no—
246C2×C3×D4C2×D412yes—
247C2×C3×D4C2×D412yes—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—24no—
255C22×C3×C4—24no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—81no—
260C22×C3×C4—81no—
261C22×C3×C4—81no—
262C22×C3×C4—81no—
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2×D412yes—
269C22×C3×C4C2×D412yes—
270C22×C3×C4C2411yescharacteristic
271C3×D8—44no—
272C3×D8—44no—
273C3×M16—44no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—44no—
285C2×C3×C8#4112yes—
286C2×C3×C8#4112yes—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—24no—
289C3×C4⋊C4—22no—
290C3×C4⋊C4—22no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—81no—
300C3×C4⋊C4—81no—
301C3×C4⋊C4C2×D412yes—
302C3×C4⋊C4C2×D412yes—
303C3×C22⋊C4—24no—
304C3×C22⋊C4—24no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—22no—
307C3×C22⋊C4—24no—
308C3×C22⋊C4—24no—
309C3×C22⋊C4—42no—
310C3×C22⋊C4—81no—
311C3×C22⋊C4—81no—
312C3×C22⋊C4—81no—
313C3×C22⋊C4—81no—
314C3×C22⋊C4—81no—
315C3×C42—21no—
316C3×C42—21no—
317C3×C42—21no—
318C3×C42—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4C23×C311yescharacteristic
325C22×D4C23×C311yescharacteristic
326C22×D4C23×C311yescharacteristic
327C23×C4—21no—
328C23×C4—21no—
329C23×C4C23×C311yescharacteristic
330C2×D8—22no—
331C2×D8—22no—
332C2×D8—22no—
333C2×D8—22no—
334C2×D8—41no—
335C2×D8—41no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—41no—
339C22×C8—22no—
340C22×C8—22no—
341C22×C8—41no—
342C22×C8C23×C311yescharacteristic
343C22×C8C23×C311yescharacteristic
344C22×C8C23×C311yescharacteristic
345C22×C8C23×C311yescharacteristic
346#127—22no—
347#127—22no—
348#125—22no—
349#125—22no—
350#123—28no—
351#123—28no—
352#121—28no—
353#121—28no—
354#121—22no—
355#121—22no—
356#121—22no—
357#121—22no—
358#121C3×D414yes—
359#121C3×D414yes—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—22no—
364#117—22no—
365#117—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4C3×D411yescharacteristic
371C2×C4⋊C4C3×D411yescharacteristic
372C2×C4⋊C4C23×C311yescharacteristic
373C2×C4⋊C4C23×C311yescharacteristic
374C2×C4⋊C4C23×C311yescharacteristic
375C2×C4⋊C4C23×C311yescharacteristic
376C2×C4⋊C4C23×C311yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4C3×D411yescharacteristic
388C2×C22⋊C4C3×D411yescharacteristic
389C2×C42C23×C311yescharacteristic
390C2×C42C23×C311yescharacteristic
391#107—22no—
392#106—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398#102—22no—
399#102—41no—
400#102—41no—
401#95—21no—
402#95—21no—
403#95—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3#12012yes—
432C23×C3C22×D411yescharacteristic
433C3×D4—22no—
434C3×D4—22no—
435C3×D4—22no—
436C3×D4—22no—
437C3×D4—41no—
438C3×D4—41no—
439C3×D4—41no—
440C3×D4—41no—
441C3×D4—41no—
442C3×D4—41no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4—84no—
446C3×D4—84no—
447C3×D4—84no—
448C3×D4—84no—
449C3×D4—84no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—84no—
484C2×C3×C4—84no—
485C2×C3×C4#12012yes—
486C2×C3×C4C22×D411yescharacteristic
487C2×C3×C4C22×D411yescharacteristic
488C2×C3×C4C2×#4111yescharacteristic
489C2×C3×C4C2×#4111yescharacteristic
490C2×C3×C4H(5,𝔽2)11yescharacteristic
491C2×C3×C42−1+411yescharacteristic
492C3×C8—22no—
493C3×C8—22no—
494C3×C8—41no—
495C3×C8—41no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24C2×C3×D411yescharacteristic
500C2×D4—24no—
501C2×D4—24no—
502C2×D4—24no—
503C2×D4—24no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—42no—
521C2×D4—81no—
522C2×D4—81no—
523C2×D4—81no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4—81no—
527C2×D4—81no—
528C2×D4—81no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4C2×C3×D412yes—
532C2×D4C2×C3×D412yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—81no—
548C22×C4C2×C3×D411yescharacteristic
549C22×C4C2×C3×D411yescharacteristic
550C22×C4C2×C3×D411yescharacteristic
551C22×C4C2×C3×D411yescharacteristic
552C22×C4C2×C3×D411yescharacteristic
553C22×C4C2×C3×D412yes—
554C22×C4C2×C3×D412yes—
555C22×C4C24×C311yescharacteristic
556D8—44no—
557D8—44no—
558M16—44no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—44no—
570C2×C8C3×#4112yes—
571C2×C8C3×#4112yes—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—81no—
585C4⋊C4—81no—
586C4⋊C4C2×C3×D412yes—
587C4⋊C4C2×C3×D412yes—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—81no—
599C22⋊C4—81no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—21no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3C2×#12011yescharacteristic
633C22×C3#53211yescharacteristic
634C22×C3#53711yescharacteristic
635C22×C3#57611yescharacteristic
636C22×C3#57611yescharacteristic
637C22×C3#57611yescharacteristic
638C22×C3#57711yescharacteristic
639C3×C4—22no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—42no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—42no—
646C3×C4—81no—
647C3×C4—81no—
648C3×C4—81no—
649C3×C4#54611yescharacteristic
650C3×C4#54611yescharacteristic
651C3×C4#54711yescharacteristic
652C3×C4#54711yescharacteristic
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—22no—
660C23—22no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23C3×#12012yes—
681C23C22×C3×D411yescharacteristic
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—84no—
695D4—84no—
696D4—84no—
697D4—84no—
698D4—84no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4C3×#12012yes—
735C2×C4C22×C3×D411yescharacteristic
736C2×C4C22×C3×D411yescharacteristic
737C2×C4C2×C3×#4111yescharacteristic
738C2×C4C2×C3×#4111yescharacteristic
739C2×C4C3×H(5,𝔽2)11yescharacteristic
740C2×C4C3×2−1+411yescharacteristic
741C8—22no—
742C8—22no—
743C8—41no—
744C8—41no—
745C2×C3—42no—
746C2×C3—82no—
747C2×C3—82no—
748C2×C3—161no—
749C2×C3#243011yescharacteristic
750C2×C3#300811yescharacteristic
751C2×C3#301211yescharacteristic
752C2×C3#317611yescharacteristic
753C2×C3#317911yescharacteristic
754C2×C3#325711yescharacteristic
755C2×C3#325911yescharacteristic
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22C2×C3×#12011yescharacteristic
785C22C3×#53211yescharacteristic
786C22C3×#53711yescharacteristic
787C22C3×#57611yescharacteristic
788C22C3×#57611yescharacteristic
789C22C3×#57611yescharacteristic
790C22C3×#57711yescharacteristic
791C4—22no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—41no—
796C4—41no—
797C4—42no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4C3×#54611yescharacteristic
802C4C3×#54611yescharacteristic
803C4C3×#54711yescharacteristic
804C4C3×#54711yescharacteristic
805C3#2550811yescharacteristic, direct product factor, Sylow
806C2—42no—
807C2—82no—
808C2—82no—
809C2—161no—
810C2C3×#243011yescharacteristic
811C2C3×#300811yescharacteristic
812C2C3×#301211yescharacteristic
813C2C3×#317611yescharacteristic
814C2C3×#317911yescharacteristic
815C2C3×#325711yescharacteristic
816C2C3×#325911yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×#540C2semidirect
2. C2×C3×#469C2semidirect
3. C2×C3×#466C2semidirect
4. C3×#2624C2semidirect
5. C3×#2059C2semidirect
6. C3×#2041C2semidirect
7. C3×#2025C2semidirect
8. C3×#2011C2semidirect
9. C3×#1895C2semidirect
10. C3×#1893C2semidirect
11. C3×#1879C2semidirect
12. C3×#1879C2semidirect
13. C3×#1864C2semidirect
14. C3×#1862C2semidirect
15. C3×#1729C2semidirect
16. #25508C3direct (N × H)
64. C2×#540C2×C3semidirect
65. C2×#469C2×C3semidirect
66. C2×#466C2×C3semidirect
67. #2624C2×C3semidirect
68. #2059C2×C3semidirect
69. #2041C2×C3semidirect
70. #2025C2×C3semidirect
71. #2011C2×C3semidirect
72. #1895C2×C3semidirect
73. #1893C2×C3semidirect
74. #1879C2×C3semidirect
75. #1879C2×C3semidirect
76. #1864C2×C3semidirect
77. #1862C2×C3semidirect
78. #1729C2×C3semidirect
805. C3#25508direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#5402
C2×C3×#4692
C2×C3×#4662
C3×#26242
C3×#20592
C3×#20412
C3×#20252
C3×#20112
C3×#18952
C3×#18932
C3×#18792
C3×#18642
C3×#18622
C3×#17292
#255083